I'd call the hospital admitting office. When I was in the Casper hospital overnight last year, they had the rates of all the nearby hotels for my wife and were able to tell her which were closest, which would take a pet, etc.
Now for a hint: Take an expired credit card and when it doesn't work, cry.
My wife had misplaced her Discover Card a couple years ago and had it replaced, then found it and put it in her desk drawer next to the new one. When we headed off to Casper she grabbed it, thinking both were the same. (They both had the same number.) But when she went to use it at the hotel it was refused. She had like $45 cash on her, and the room was $90 or so. So she's standing there, tears running down her cheeks, husband in the hospital, nowhere to sleep except the car, and it's 10 degrees out. They gave her the room for $35!
I had cash and debit cards in my wallet, which she had in her purse, but she didn't think about that.
We both stayed there the next night for ~$90 -- figured they deserved at least one night from us at full rate.